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# if slope of one of the lines given by ax 2+2hxy+by 2=0 is three times the other then the condition for h is

Aakanksha Talreja
34 Points
6 years ago
divide d given equation by $x^{2}$ and let y/x be slope m hence we get $bm^{2}+2hm+a=0$
nw, let d roots of this equation be$m_{1} , m_{2}$ as given $m_{1} =3 m_{2}$ nw SOR = m1 + m2=-2h/b=4m2
POR=m1m2=$3 m_{2}^{2}$ = a/b therefore, $m_{2}=\sqrt{a/3b}$ , $m_{2}=\sqrt{a/3b}= - h/2b \therefore h=-2\sqrt{ab/3}$